Adding Vectors: Find Resultant Magnitude of P + S

[leetnerdgirl]

Okay I've been given a question about adding and subtracting vectors, and my physics teacher didn't even explain anything at all.

Q1) What is the magnitude of the resultant of the addition of the vector P + S? Where P is 2 units north and S is 5 units east.

I think I'd have to use Pythagoras' Theorem but seriously, I have no idea how to do this so if someone could PLEASE explain in detail and go through all the steps that would be awesome.
Thanks.

 

[mplayer]

Draw it out on a coordinate system, and know that vectors P,S add head-to-tail. With this you can set up a triangle, and solve for the resultant vector, R. The constant of that resultant vector is the magnitude of that vector.

Ultimately, you could have just used the squareroot of the sum of the squares deal to get it from the start, but draw it out so you understand the concept of vector addition.

 

[Matt H]

Your magnitude will be the Sqrt. of (2^2 + 5^2) which equals 5.39 units. It's basically the pythagorean thm. If you draw the vectors out you will have a leg 2 units long pointing straight up (north) and then you will have another leg 5 units long pointing in the right direction (east). Since you have the values of the two "legs" you can look at the magnitude of the vector as the hypoteneuse of the triangle. Therefore in your case P^2 + S^2 = C^2, solve for C and there is your magnitude.



Edit: It will look like this crappy rendering below (each dash = 1 unit), just connect the two ends with a hypoteneuse and solve for the length of it.


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